In Acts 16:31 the word "believe" is in the aorist tense (undefined action). In Acts 16:34 the word "believe" is in the perfect tense. What conclusions can be drawn exegetically from the change in verb ...

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But to all who did receive him, who believed in his name, he gave the right to become children of God, John 1:12 ESV
But to all who have received him ...